What is fastest way to travel in Harry Potter universe?

As the question title says, what's the fastest way to travel in the Harry Potter universe?

Answer

In the order of increased fastness:

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  Floo network:

  
  

  Definitely not instantaneous, but pretty fast:

  
  

  
  

  'But don't panic and get out too early, wait until you see Fred and George.' (CoS)

  
  

  
  


• 
  
  

  Portkey:

  
  

  Seems to be a couple of seconds:

  
  

  
  

  It happened immediately: Harry felt as though a hook just behind his navel had been suddenly jerked irresistibly forwards. His feet had left the ground; he could feel Ron and Hermione on either side of him, their shoulders banging into his; they were all speeding forwards in a howl of wind and swirling colour; his forefinger was stuck to the boot as though it was pulling him magnetically onwards and then –
  His feet slammed into the ground; Ron staggered into him and he fell over; the Portkey hit the ground near his head with a heavy thud. (GoF)

  
  

  
  


• 
  

  Apparition:

  
  

  This seems the fastest subjectively, but of course, given overall JKR Maths proficiency, she wasn't as precise as one would have preferred for numerical comparisons:

  
  
  

  
  

  Harry felt Dumbledore's arm twist away from him and redoubled his grip; the next thing he knew, everything went black; he was being pressed very hard from all directions; he could not breathe, there were iron bands tightening around his chest; his eyeballs were being forced back into his head; his eardrums were being pushed deeper into his skull and then –
  He gulped great lungfulls of cold night air and opened his streaming eyes.

  
  

  
  

  and

  
  

  
  

  Twycross stepped forwards, turned gracefully on the spot with his arms outstretched and vanished in a swirl of robes, reappearing at the back of the Hall. 'Remember the three Ds,' he said, 'and try again... one – two – three –'

  
  

  
  

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Also, there are two more ways to travel near-instantaneously:

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  Vanishing cabinet. We don't know how fast it transports you or if it's using one of the 3 methods above (no canon info), but presumably it's as fast as the other methods.

  
  


• 
  

  As @Kushtrim P. noted in a comment, you can use time-turner+normal travel method (your speed of spacial travel may be as slow as you want, but absolute arrival time is arbitrarily small due to temporal displacement). That is indeed a very well known method of travel in Science Fiction.